To solve the equation, we need to simplify the expression on the right side first:

17/2 - (-3/7 + 5/3)

To add fractions, we need a common denominator. The least common multiple of 2, 7, and 3 is 42.

17/2 - (-3/7 + 5/3) = 17/2 - (-9/42 + 35/42)

Now, we can add the fractions:

17/2 - (-9/42 + 35/42) = 17/2 - 26/42

To subtract fractions, we need a common denominator. The least common multiple of 2 and 42 is 42.

17/2 - 26/42 = 357/42 - 26/42

Now, we can subtract the fractions:

357/42 - 26/42 = 331/42

Now, we can substitute this simplified expression back into the original equation:

x - (331/42) = -1/3

To isolate x, we need to move (331/42) to the other side of the equation:

x = -1/3 + 331/42

To add fractions, we need a common denominator. The least common multiple of 3 and 42 is 126.

x = -1/3 + (331/42)(3/3)

x = -1/3 + 993/126

Now, we can add the fractions:

x = -1/3 + 993/126

To simplify the fractions, we can find a common denominator:

x = -42/126 + 993/126

Now, we can add the fractions:

x = (993 - 42)/126

x = 951/126

Now, we can simplify the fraction:

x = 79/10

Therefore, the solution to the equation is x = 79/10.